Is there any food at the Met Museum ? Are any restaurants or cafeterias open ?

No

Walk down to 3 Ave. Lots of local eats and cheaper.

What Elizabeth said, but don't do it. It's a trap. I paid 30 dollars for a water a sandwich and fries. Go outside and get food from a street vendor. It'll taste better and it won't cost your firstborn.

Yes. There is the Eatery on the ground floor and the American Wing Cafe on the 1st floor. They are open sat-mon 11-4 and thurs-fri 1-6.